Toán Lớp 11: tan2x=tan(x+pi/4). giúp e vs ạ

Question

Toán Lớp 11:  tan2x=tan(x+pi/4). giúp e vs ạ

cobelolen · Answer

~rai~        ( tan2x= tan left(x+ dfrac{ pi}{4} right) quad(1)  ĐKXĐ: begin{cases} cos2x ne 0   cos left(x+ dfrac{ pi}{4} right) ne 0 end{cases}   Leftrightarrow  begin{cases}2x ne  dfrac{ pi}{2}+k pi  x+ dfrac{ pi}{4} ne dfrac{ pi}{2}+k pi end{cases}   Leftrightarrow  begin{cases}x ne  dfrac{ pi}{4}+k dfrac{ pi}{2}  x ne dfrac{ pi}{4}+k pi end{cases}   Leftrightarrow x ne dfrac{ pi}{4}+k dfrac{ pi}{2}.(k in mathbb{Z})  (1) Leftrightarrow 2x=x+ dfrac{ pi}{4}+k pi   Leftrightarrow x= dfrac{ pi}{4}+k pi. text{(kh&ocirc;ng thỏa m&atilde;n)}   text{Vậy S=} varnothing. )

thucquyenlan · Answer

Điều kiện:   $ begin{array}{l}  left {  begin{array}{l}  cos 2x  ne 0    cos  left( {x +  dfrac{ pi }{4}}  right)  ne 0  end{array}  right.  Leftrightarrow  left {  begin{array}{l} 2x  ne  dfrac{ pi }{2} + k pi    x +  dfrac{ pi }{4}  ne  dfrac{ pi }{2} + k pi   end{array}  right.  Leftrightarrow x  ne  dfrac{ pi }{4} +  dfrac{{k pi }}{2}    tan 2x =  tan  left( {x +  dfrac{ pi }{4}}  right)     Leftrightarrow 2x = x +  dfrac{ pi }{4} + k pi      Leftrightarrow x =  dfrac{ pi }{4} + k pi  left( {k  in  mathbb{Z}}  right)  end{array}$   Đối chiếu với điều kiện $x in  emptyset$